GB2115969A

GB2115969A - Aid for teaching mathematics

Info

Publication number: GB2115969A
Application number: GB08201404A
Authority: GB
Inventors: Arthur Robert O'malley
Original assignee: MALLEY ARTHUR ROBERT O
Current assignee: MALLEY ARTHUR ROBERT O
Priority date: 1982-01-19
Filing date: 1982-01-19
Publication date: 1983-09-14

Abstract

A teaching aid is in the form of a conventional calculator in combination with a means 3 for measuring angles and registering them on the calculator so that their trigonometrical functions can be determined. Means 4 for measuring lengths and registering them on the calculator may also be included. The measuring means 3,4 may each comprise a magnetic tape having a series of magnetised and unmagnetised regions which are counted. The angle measuring means comprises an arm pivoted at (1), a key (3) moving with the arm and being actuated by pressing the arm downwards thereby causing the angle to be read and displayed on the calculator e.g. as a trigonometrical function. <IMAGE>

Description

SPECIFICATION Aid for teaching mathematics This invention relates to the teaching of mathematics, which has long presented probiems to pedagogues. In particular, the related branches geometry and trigonometry were at one time almost exclusively taught in schools on a purely theoretical basis and only vaguely related to the practicalities of such uses as surveying and navigation. In more recent years, more practical methods of teaching have been sought, but useful teaching aids are not readily available.

Suitable teaching aids would enable trigonometry and geometry to be taught axiomatically. For this to be done, it is essential that the student of these subjects should be able to study both mathematical processes and their resultant functions in their proper setting and realistic dimensions. To do this, it is essential that modern teaching be freed from the false dimensions imposed by the use of rule and exercise book and the traditional 'plane' method by which the subjects are taught and in which a great deal of both teachers' and students' time is occupied in the drawing of geometrical shapes in a plane surface. A great deal more of their time is devoted to providing by theorem the form that a flat shape would assume in its natural dimensions.In view of the nature of the instruments used in its implementation, this method of tuition will continue until freed by modern apparatus capable of benefiting education by removing the abstract element and replacing it with reality.

Those who teach and learn are surrounded by what they are studying, including distances, heights, squares, angles and surfaces. Outside the classroom there are greater distances and heights, all of them a monument to Man's ability to measure.

The present invention provides a teaching aid comprising a conventional electronic calculator of the type that includes trigonometrical functions, in combination with a pair of pivotally connected arms, one of which is preferably fixed with respect to the calculator, and means included in the circuit of the calculator for registering, on the actuation of an appropriate key, the angle between the arms or a trigonometrical function of that angle.

The teaching aid may also comprise a pull-out rule for measuring lengths, with means included in the circuit of the calculator for registering, upon actuation of an appropriate key, the length being measured by the rule.

The calculator will normally also include a set of keys for carrying out calculations of the type for which calculators are conventionally used.

Instead of a pair of pivotally connected arms, the calculator may bear a single arm pivotally connected to it, the angle registered then being the angle between the arm and a fixed line on the body of the calculator.

A sight can be included to facilitate lining up the movable arm with a distant object.

The means for registering the angle and, if appropriate, the length measured by the device could be, for example, a magnetic tape in which a series of magnetized and unmagnetized regions corresponded to units of angular or longitudinal measurement, e.g. degrees and millimetres respectively.

Actuation of the appropriate control would enable the number of regions to be counted and the number, or a desired function of it, read off the calculator display. This type of means would enable negative as well as positive angles and lengths to be registered, if desired.

The accompanying drawings show a device in accordance with the present invention. A perspective view of one side of a calculator is shown in Figure 1 the other side is of conventional design. A view along arrow II is shown in Figure 2.

Pivot 1 for an arm (not shown) and scale 2 graduated from 0 to 90 form the part of the device for measuring angles. A key 3 moves round with the arm and is actuated by pressing the arm downwardly, causing the angle to be read off on the display of the calculator. By actuating a trigonometric function key on the unshown face of the calculator, that function of the angle can be read.

Similarly, the distance that a pull-out tape 4 is extended can be read off from the two circular scales 5 and 6 and can be read off the calculator display by actuating central knob 7.

The relationships between the sides of the trigo nometricfunctions of the angles of triangles can thus be readily demonstrated using a device in accordance with the present invention.

1. Ateaching aid comprising a conventional electronic calculator of the type that includes trigonometrical functions, in combination with a pair of pivotally connected arms or with a single arm pivotally connected to the calculator, and means included in the circuit of the calculator for registering, on the actuation of an appropriate key, the angle between the arms or between the single arm and a datum line on the calculator, or a trigonometrical function of that angle.

2. Ateaching aid as claimed in Claim 1, also comprising a pull-out rule for measuring lengths, with means included in the circuit of the calculator for registering, upon actuation of an appropriate key, the length being measured by the rule.

3. Ateaching aid as claimed in Claim 1 or 2, in which the calculator includes a set of keys for carrying out calculations of the type for which calculators are conventionally used.

4. Ateaching aid as claimed in any preceding claim, including a sight to facilitate lining up the movable arm with a distant object.

5. A teaching aid as claimed in any preceding claim, in which the means for registering the angle and, if appropriate, the length measured by the device is a magnetic tape in which a series of magnetized and unmagnetized regions corresponded to units of angular or longitudinal measurement so that actuation of the appropriate control would enable the number of regions to be counted and the number, or a desired function of it, read off

**WARNING** end of DESC field may overlap start of CLMS **.

Claims

**WARNING** start of CLMS field may overlap end of DESC **. SPECIFICATION Aid for teaching mathematics This invention relates to the teaching of mathematics, which has long presented probiems to pedagogues. In particular, the related branches geometry and trigonometry were at one time almost exclusively taught in schools on a purely theoretical basis and only vaguely related to the practicalities of such uses as surveying and navigation. In more recent years, more practical methods of teaching have been sought, but useful teaching aids are not readily available. Suitable teaching aids would enable trigonometry and geometry to be taught axiomatically. For this to be done, it is essential that the student of these subjects should be able to study both mathematical processes and their resultant functions in their proper setting and realistic dimensions. To do this, it is essential that modern teaching be freed from the false dimensions imposed by the use of rule and exercise book and the traditional 'plane' method by which the subjects are taught and in which a great deal of both teachers' and students' time is occupied in the drawing of geometrical shapes in a plane surface. A great deal more of their time is devoted to providing by theorem the form that a flat shape would assume in its natural dimensions.In view of the nature of the instruments used in its implementation, this method of tuition will continue until freed by modern apparatus capable of benefiting education by removing the abstract element and replacing it with reality. Those who teach and learn are surrounded by what they are studying, including distances, heights, squares, angles and surfaces. Outside the classroom there are greater distances and heights, all of them a monument to Man's ability to measure. The present invention provides a teaching aid comprising a conventional electronic calculator of the type that includes trigonometrical functions, in combination with a pair of pivotally connected arms, one of which is preferably fixed with respect to the calculator, and means included in the circuit of the calculator for registering, on the actuation of an appropriate key, the angle between the arms or a trigonometrical function of that angle. The teaching aid may also comprise a pull-out rule for measuring lengths, with means included in the circuit of the calculator for registering, upon actuation of an appropriate key, the length being measured by the rule. The calculator will normally also include a set of keys for carrying out calculations of the type for which calculators are conventionally used. Instead of a pair of pivotally connected arms, the calculator may bear a single arm pivotally connected to it, the angle registered then being the angle between the arm and a fixed line on the body of the calculator. A sight can be included to facilitate lining up the movable arm with a distant object. The means for registering the angle and, if appropriate, the length measured by the device could be, for example, a magnetic tape in which a series of magnetized and unmagnetized regions corresponded to units of angular or longitudinal measurement, e.g. degrees and millimetres respectively. Actuation of the appropriate control would enable the number of regions to be counted and the number, or a desired function of it, read off the calculator display. This type of means would enable negative as well as positive angles and lengths to be registered, if desired. The accompanying drawings show a device in accordance with the present invention. A perspective view of one side of a calculator is shown in Figure 1 the other side is of conventional design. A view along arrow II is shown in Figure 2. Pivot 1 for an arm (not shown) and scale 2 graduated from 0 to 90 form the part of the device for measuring angles. A key 3 moves round with the arm and is actuated by pressing the arm downwardly, causing the angle to be read off on the display of the calculator. By actuating a trigonometric function key on the unshown face of the calculator, that function of the angle can be read. Similarly, the distance that a pull-out tape 4 is extended can be read off from the two circular scales 5 and 6 and can be read off the calculator display by actuating central knob 7. The relationships between the sides of the trigo nometricfunctions of the angles of triangles can thus be readily demonstrated using a device in accordance with the present invention. CLAIMS

5. A teaching aid as claimed in any preceding claim, in which the means for registering the angle and, if appropriate, the length measured by the device is a magnetic tape in which a series of magnetized and unmagnetized regions corresponded to units of angular or longitudinal measurement so that actuation of the appropriate control would enable the number of regions to be counted and the number, or a desired function of it, read off the calculator

6. Ateaching aid as claimed in Claim 1 substantially as hereinbefore described with reference to the accompanying drawings.